Commercial wafer based solar cells are made from typically 10×10 cm2 up to 22×22 cm2 silicon wafers. As illustrated in FIG. 1, a cast multicrystalline silicon block 2 (also known as an ingot), typically 1×1×0.7 m3 in size, is sawn into square (10×10 cm2 up to 22×22 cm2) shaped columns 4 (commonly known as bricks), which are then sawn into individual wafers 6, each typically 120-250 μm thick. An ingot is usually sawn into 4×4 or 5×5 bricks. Solar cells can be made from multicrystalline silicon or monocrystalline silicon, with different techniques used for growing multicrystalline and monocrystalline silicon ingots.
For wafer manufacturers it is of interest to characterise the electronic and structural properties of ingots or bricks prior to wafer slicing. It is commonly known that cast multicrystalline (mc) silicon ingots have increased impurity concentration within the silicon in the outside regions of the ingot, i.e. at the bottom, top and sides. At the bottom and the sides this is the result of diffusion of impurities from the crucible walls into the ingot, while at the top it is caused by segregation of impurities towards the upward-moving top liquid phase during crystallisation of the ingot. A result of the increased impurity concentration is reduced electronic material quality, described by a lower effective minority carrier lifetime. FIG. 2 shows in side view a typical effective minority carrier lifetime distribution in a cast mc silicon ingot, showing an area of mostly high effective lifetime material 8 in the centre and regions of low lifetime 10 at the top, bottom and sides.
Experimental techniques that are currently in use for characterisation of bricks include infrared (IR) transmission and minority carrier lifetime scanning. In the former technique, the transmission of sub-band gap light through the brick is measured from different directions with an IR camera that is sensitive to the sub band-gap spectral range (wavelengths>1100 nm for silicon), providing three-dimensional information about the density and position of inclusions such as silicon carbide (SiC) and silicon nitride (Si3N4).
Several experimental techniques exist for measuring the effective minority carrier lifetime, including both transient and quasi steady state photoconductance (QSSPC) and microwave photoconductance decay (μ-PCD). These techniques measure the effective minority carrier lifetime, which is an effective sample characteristic parameter affected by both the bulk material quality (i.e. the bulk minority carrier lifetime) and surface recombination. Especially on samples with unpassivated surfaces, such as as-cut wafers, the effective lifetime is usually strongly affected or dominated by surface recombination. Two-dimensional information about lateral variations of the effective lifetime, e.g. on one surface of a brick, can be obtained by using the above methods in a scanning mode, generating a map via point by point scanning in a manual or automated fashion. In some cases, such as QSSPC, the measured effective lifetime data can be converted into bulk lifetime data over a limited range by using predetermined relationships between bulk lifetime and effective lifetime.
Although the effective minority carrier lifetime is the more easily measured quantity, the bulk minority carrier lifetime is the more important quantity for photovoltaic applications because: (a) the impact of surface recombination is significantly reduced in subsequent processing via removal of low lifetime surface material and surface passivation; and (b) bulk lifetime, unlike effective lifetime on an unpassivated sample, determines both the voltage and the current of a finished solar cell. Especially for unpassivated samples with high surface recombination, it is therefore important to be able to convert an as-measured effective lifetime to bulk lifetime.
Another important aspect of minority carrier lifetime is its dependence on the injection level. The bulk lifetime is determined by various recombination mechanisms, including defect recombination, radiative recombination and Auger recombination. The recombination rate via these mechanisms is non-linear in the concentration of minority carriers and as a result the bulk minority carrier lifetime itself depends on the density of minority carriers. Ideally therefore, experimental data for the minority carrier lifetime should be reported as a function of injection level, whether lifetime is area-averaged or spatially resolved. However, since representation of data as a function of two independent parameters (position and injection level) is difficult, spatially resolved data such as lifetime images or lifetime maps are often reported only for a single injection level for each point.
Upgraded Metallurgical Grade (UMG) silicon is a prospective material for achieving significant cost reductions in silicon wafer-based photovoltaics. A commonly observed feature of UMG ingots and bricks is an inversion of the background doping density that occurs from the bottom to the top of an ingot, caused by the presence of significant quantities (densities) of both phosphorous and boron in the feedstock. Due to the different segregation coefficients of these dopants, their incorporation into the crystal occurs at different rates. As a result UMG ingots are generally found to be p-type at the bottom and n-type at the top, with a so called ‘compensated region’ in between that is effectively undoped or only very lightly doped. A method to gain information quickly about the position and shape of the transition region is required, since wafers from that region and the n-type wafers from above that region cannot be used in conventional screen printed solar cell production lines, which normally use p-type wafers.
The ability to measure the effective lifetime of silicon wafers using photoluminescence (PL) imaging has been described in published PCT patent application No WO 2007/041758 A1 entitled ‘Method and System for Inspecting Indirect Bandgap Semiconductor Structure’ and incorporated herein by reference. The measurable luminescence intensity in PL imaging on semiconductor materials is determined by the rate of spontaneous emission rsp, which can generally be assumed to be linear in the product of the electron (n) and hole (p) concentrations, i.e. rsp=B*n*p, where B is a proportionality factor referred to in the literature as the radiative recombination coefficient. In PL imaging applications on silicon samples, particularly on unpassivated surfaces, the condition of low level injection is generally fulfilled, which means that the excess minority carrier concentration Δn is significantly smaller than the background doping concentration Nd, i.e. Δn<<Nd. In this case the total minority carrier density is given to very good approximation by Δn and the majority carrier density by Nd. As a result the emitted luminescence is proportional to the excess minority carrier density and the background doping density so that rsp=B*Δn*Nd. Under quasi steady state conditions, i.e. where the generation and recombination rates are equal, the effective minority carrier lifetime is inversely proportional to the generation rate G and proportional to the minority carrier density such that τeff=Δn/G, which results in rsp=B*G*τeff*Nd. The rate of spontaneous emission and thereby the PL intensity under specific illumination intensity (i.e. for given G) is thus proportional to the product of the effective minority carrier lifetime and the doping density.
In previous PL imaging applications the influence of the doping density on PL intensities has been described, but an implicit assumption of laterally constant background doping density over the sample area was made. For example in T. Trupke, R. A. Bardos and J. Nyhus, ‘Photoluminescence characterisation of silicon wafers and silicon solar cells’, 18th Workshop on Crystalline Silicon Solar Cells & Modules 2008, Vail, USA, the influence of the background doping density on the absolute luminescence intensity between different samples and its impact on the calibration of PL images has been discussed. For many commonly used silicon wafers (e.g. conventional cast mc wafers) the assumption that the background doping density is constant laterally across the sample area is well justified, allowing interpretation of PL images in terms of lateral variations of the excess minority carrier density Δn in all cases where the surface properties of the sample (texturing and antireflection coating) are sufficiently homogeneous.
However there are several types of sample where the assumption of a laterally constant background doping density is not justified. These include:
(i) Side facets of common mc silicon bricks or ingots. Doping density variations ND(x) within typical mc silicon bricks and ingots can often be significant. In many cases the variation of the doping density along the growth direction can be described by the Scheil equation which is derived from considering the thermodynamic potential of the dopant in the two phases of the solidifying silicon casting block:ND(x)=ND(0)·Keff(1−x)Keff−1 
In this equation Keff is a coefficient characteristic of the dominant dopant atom and the crystal host and x is the relative height within the brick or ingot (x=0 corresponds to the bottom, x=1 to the top). For example for a typical 25 cm high boron doped (p-type) silicon ingot or brick, the doping density increases by typically 30%-40% relative from the bottom to the top.
(ii) Side facets of UMG silicon bricks or otherwise intentionally or unintentionally doping-compensated ingots or bricks. Strong variations of the effective doping density are observed, with a transition region from effective p-type doping to n-type doping.
(iii) Wafers from UMG bricks. The transition region from p-type to n-type is not strictly parallel to the direction in which wafers are cut from the ingot, because of a typically curved solid-liquid interface near the crystallisation front. Wafers from near the transition region will therefore show strong variations in the doping density within each wafer, some of them even showing a transition from p-type to n-type within a single wafer.
(iv) Vertical samples from Czochralsky (Cz) grown monocrystalline ingots. Vertical variations in the background doping density will show up on PL images taken on silicon ingots or wafers cut vertically from such ingots.
(v) Monocrystalline wafers, particularly n-type Cz wafers, often exhibit circular variations (striations) in the doping density. These can be seen particularly clearly in luminescence images taken on unpassivated wafers, since the effective lifetime is surface limited and thus almost constant across the wafer area. Even small variations in doping density are therefore clearly visible in luminescence images.
(vi) There are various other new and more exotic types of silicon ingot manufacturing processes in development that may become mainstream. Examples include BP Solar's cast ‘mono-crystalline’ process and Muto's direct chemical formation process. Each new process for making crystalline silicon blocks will have idiosyncrasies in dopant concentrations and lifetime variations.
Where a constant background doping density can no longer be assumed, the intensity variation in a PL image is determined by the product of 1) the doping density and 2) the effective minority carrier lifetime. To get reliable information about spatial variations of one of these two quantities, the PL signal therefore needs to be corrected or normalised for absolute or relative variations of the other quantity, which can be measured directly or inferred.